Question

Decimal expansion of which of the following is non terminating recurring.

1.
$\frac{2}{5}$
2.

$\frac{3}{16}$

3.
$\frac{3}{11}$

4.
hard one

$\frac{137}{25}$

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Answer 1

Answer:

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$\frac{2}{5} = 0.4$

$\frac{3}{16} = 0.1875$

$\frac{3}{11} = 3.66$

$\frac{137}{25} = 5.48$

Step-by-step explanation:

@ItzStarBrainly

Answer 2

Answer:

$\:$

(1) 2/5

The denominator = 5

Since 5 is the only number which is prime is present in the denominator

Hence the decimal expansion is terminating

The denominator is 16

(2) 3/16

16=2×2×2×2

Since 2 is the only number which is prime , is present in the prime factorisation of the denominator

Hence the decimal expansion is terminating

(3) 3/11

Denominator = 11 = 1 x 11

Since, the denominator is other than prime factors 2 or 5.

∴ the decimal expansion of 3/11 will be non terminating recurring.

(4) (137/25)

The denominator is 25

25=5×5

Since 5 is the only number which is prime , is present in the prime factorisation of the denominator

Hence the decimal expansion is terminating

RESULT:-

Hence the required fraction which has non-terminating recurring is 3/11

☆hope this helps ☆